If you were fixing cars, then you could call a mistake if you put the wrong oil in the engine. That you would need to cover.
But if you changed the oil, and the oil turned out to be "bad" ( for a lack of a better term ), then the oil had bugs in it. It was flawed.
Updates: Additional photography sittings, design modifications, bug fixes.
Mistakes: Lost data, work that is later found to not meet the spec.
But in the end, it all comes down to how you want to run your business. If you charge the customer for whatever extra you're doing, what's going to be the result of this? Are you going to chase them off? Get a bad recommendation? Is there no harm at all?
Depending on that outcome and what you want, you can probably find the answer as to whether you should cover it or not.
Creating software is a creative process, and there is rarely an end point where the software is completely bug-free, or where there is absolutely no further improvement which can be made.
Bugs are like flubbed lines. They happen. They always happen. And coders get paid for fixing them.
If your doctor makes a mistake, does he give you a refund? Or does he charge both for the mistake and the new fix? Your lawyer?
Unless tests, QA and the like were listed on the requirements list, I believe most fixes should be charged, too. Of course when tests are required and written according to the contract, and obvious bugs still fall through the cracks, that is an entirely different matter.
This is a difficult subject imho, because most employers are not willing to pay for testing and, unfortunately, not for fixing the consequences, either.